My InterpretationI agree with AdrianDangerous, except the words are not those of Jack the Ripper himself. The last victim, Mary Jane Kelly, was murdered on 9th November [1888] and the song mentions the last time being the 4th.
Bearing all that in mind, this is my interpretation [in a historical fiction sense]:
a man had a relationship with Kelly, possibly in spite of her being a prostitute, and he is remembering the last time he saw her before her murder; "the blood red streaks on velvet throats" may be a reference to the fact a lot of Ripper victims had their throats slit. The man is also mourning Kelly - her death was by far the worst of the Ripper murders, as she was practically unidentifiable after the discovery of her body. I believe "I wish I could just remember your name", is a reflection of the 'putting a name to a face' thing; metaphorically speaking of course, after her death she had no face to put a name to.
But a part of this man wishes it had been him instead - "you know I don't want to live forever" and of course, "the worst [thing] is being alone" and now he is.
As for "the streetlights fanned our trail of fame through London", I can only assume that the streetlights that lead the way through the night did not help the police identify Jack the Ripper, who gained fame through these events.

My InterpretationMmm Jack the Ripper. yeah nice idea - I had never envisioned that myself. I always saw the song as a lone figure walking through a desolate/deserted devastated future London.
This guy is immortal - I presume a vampire
"they cry remember - blood red streaks on velvet throats at night"
Who is incredibly old and tired, cursed with immortality
"you know I don't want to live forever"
Who had actually loved one of his victims in Victorian London - but who had no choice but consume her life force OR who had to watch as old age/death took her
"sometimes I wish I could have taken your place my love".
That is how I always picture it.
Thanks for reading :)

General CommentIf I recall from an old interview this is actually the continuation from walk in the shadows from the same rage for order album, back in the day the band was really into the Anne Rice books, Interview with the Vampire and Lestat, it seems for a moment to be talking about Jack the ripper but it's actually about the vampire who killed the girl he was convincing to join him.

"They cry remember, blood-red streaks on
velvet throats at night"

"Sometimes I wish I could have taken your
place my love / You know I don't want to live forever"